Calculations quantum dynamical

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

Recently, two-dimensional quantum dynamical calculations using ab initio surfaces from Murrell and co-workers35,36 which span the regions that include the O-H—H conical intersections of the B 1A1 and X 1A1 surfaces... 

An overview of the time-dependent wavepacket propagation approach for four-atom reactions together with the construction of ab initio potential energy surfaces sufficiently accurate for quantum dynamics calculations has been presented. Today, we are able to perform the full-dimensional (six degrees-of-freedom) quantum dynamics calculations for four-atom reactions. With the most accurate YZCL2 surface for the benchmark four-atom reaction H2 + OH <-> H+H2O and its isotopic analogs, we were able to show the following ... 

The analytic potential energy surfaces, used for the Cl + CH3Clb and Cl + CHjBr trajectory studies described here, should be viewed as initial models. Future classical and quantum dynamical calculations of SN2 nucleophilic substitution should be performed on quantitative potential energy functions, derived from high-level ab initio calculations. By necessity, the quantum dynamical calculations will require reduced dimensionality models. However, by comparing the results of these reduced dimensionality classical and quantum dynamical calculations, the accuracy of the classical dynamics can be appraised. It will also be important to compare the classical and quantum reduced dimensionality and classical complete dimensionality dynamical calculations with experiment. 

A more general description of the effects of vibronic coupling can be made using the model Hamiltonian developed by Koppel, Domcke and Cederbaum [65], The basic idea is the same as that used in Section III.C, that is to assume a quasidiabatic representation, and to develop a Hamiltonian in this picture. It is a useful model, providing a simple yet accurate analytical expression for the coupled PES manifold, and identifying the modes essential for the non-adiabatic effects. As a result it can be used for comparing how well different dynamics methods perform for non-adiabatic systems. It has, for example, been used to perform benchmark full-dimensional (24-mode) quantum dynamics calculations... 

M. D. Coutinho Neto, A. Viel, and U. Manthe, The ground state tunneling splitting of malonaldehyde Accurate full dimensional quantum dynamics calculations. J. Chem. Phys. 121, 9207 9210 (2004). 

Another major, future advance in the quantum chemical computation of potential energy surfaces for reaction dynamics will be the ability to routinely compute the energies of molecular systems on the fly . The tedious and time-consuming process of fitting computed quantum chemical values to functional forms could be avoided if it were possible to compute the PES as needed during a classical trajectory or quantum dynamics calculation. For many chemical reactions, it should be practical in the near future to prudently select a sufficiently rapid and accurate electronic structure method to facilitate dynamics computations on the fly. 

Dynamics calculations have also provided new approaches to the stereochemical modes through which cyclopropanes and trimethylene intermediates may be related. Full quantum dynamics calculations for the trimethylene diradical based on a reduced dimensionality model that followed wave packet densities and time constants for formation of products led to the conclusion that conrotatory and disrotatory double rotations of both terminal methylene groups are favored over a single rotation of just one by a 2.2 1 ratio." °... 

B. Kohler Prof. Fleming, your experimental results clearly indicate that in the case of I2 in hexane the vibrational coherence of an initially prepared wavepacket persists for unexpectedly long times. However, quantum dynamical calculations show that wavepacket spreading due to anharmonicity can be very substantial even for isolated molecules... 

Sn2 reactions of methyl halides with anionic nucleophiles are one of the reactions most frequently studied with computational methods, since they are typical group-transfer reactions whose reaction profiles are simple. Back in 1986, Basilevski and Ryaboy have carried out quantum dynamical calculations for Sn2 reactions of X + CH3Y (X = H, F, OH) with the collinear collision approximation, in which only a pair of vibrations of the three-center system X-CH3-Y were considered as dynamical degrees of freedom and the CH3 fragment was treated as a structureless particle [Equation (11)].30 They observed low efficiency of the gas-phase reactions. The results indicated that the decay rate constants of the reactant complex in the product direction and in the reactant direction did not represent statistical values. This constitutes a... 

The Hamiltonian Eq. (7) provides the basis for the quantum dynamical treatment to be detailed in the following sections, typically involving a parametrization for 20-30 phonon modes. Eq. (7) is formally equivalent to a class of linear vibronic coupling (LVC) Hamiltonians which have been used for the description of excited-state dynamics in molecular systems [66] as well as the Jahn-Teller effect in solid-state physics. In the following, we will elaborate on the general properties of the Hamiltonian Eq. (7) and on quantum dynamical calculations based on this Hamiltonian. 

Waterland, R.L., Lester, M.I., and Halberstadt, N. (1990). Quantum dynamical calculations for the vibrational predissociation of the He-ICl complex Product rotational distribution, J. Chem. Phys. 92, 4261-4271. 

Since there are only four atoms, this case can act as a useful bridge between classical and quantum dynamics calculations. Since nonadiabatic effects are expected to be minor, the quantum calculations are limited by the PES and the computational precision. Consequently, they will ultimately offer the most meaningful comparison between experiment and theory. However, the quantum dynamics calculations carried out to date have been limited to two dimensions. Therefore, they have little to do with the HOCO system per se, except in the general sense of exploring the physics of vibrational resonances coupled to continua. 

Although apparently simple, there is a lot of subtlety in this model. The most important parameter in determining the translational energy dependence of the activation energy is AE. If we reduce AE, then the slope of E (Elmm) increases, which is found in the results of the full quantum dynamics calculations the slope is greater for the J 0 -> 4 transition than for J 0 - 6. AE is the shift in the threshold due to the thermal motion, it is the amount of energy surface motion contributes to aid the dissociation or rovibrational excitation. Why this should vary from one particular transition to... 

Because of the small size of the utilized test molecules and the fact that the molecules remain in their electronic ground states, accurate calculations of the transition frequency fluctuation correlation function of these systems fluctuations would seem to be achievable with state-of-the-art quantum dynamics calculations. 

As shown above, classical unimolecular reaction rate theory is based upon our knowledge of the qualitative nature of the classical dynamics. For example, it is essential to examine the rate of energy transport between different DOFs compared with the rate of crossing the intermolecular separatrix. This is also the case if one attempts to develop a quantum statistical theory of unimolecular reaction rate to replace exact quantum dynamics calculations that are usually too demanding, such as the quantum wave packet dynamics approach, the flux-flux autocorrelation formalism, and others. As such, understanding quantum dynamics in classically chaotic systems in general and quantization effects on chaotic transport in particular is extremely important. 

Accurate quantum dynamical calculations for reactions with deep wells have been a major challenge to theoreticians. In this regard, due to the potential well depth of 7 eV corresponding to the stable water molecule, the reaction O ( D) -p H2 OH + H poses a formidable obstacle to exact quantum dynamical treatment. As a result, the earliest quantum calculation on this reaction was carried out by Baden-hoop et al. [73] using a 2D model where the bending motion was treated by a sudden approximation. 

Among those TDQM studies, exact quantum dynamical calculations were usually limited to the total angular momentum / = 0. For / > 0, most of the authors used a capture model (or L-shift model) [77] to estimate the reaction probability from the / = 0 results. Even the direct calculations of reaction probabilities for / > 0 were performed using the centrifugal sudden (CS) approximation. Carroll... 

Quantum dynamical calculations on the IRMPE/D of 614, 615 O3. Quantum interference effects and discussion of the possibility of mode-selective excitation and reaction Confirmation that OCS does not undergo IRMPD at 616 high laser fluences (ca. 250 J cm ). Laser-induced dielectric breakdown in OCS, OCS-He, and OCS-Ar does lead to dissociation, giving CO + S Ab initio study of SO2 IRMPE using the most proba- 617 ble path approximation to select the most important paths within the semiclassical Floquet matrix. Conclude that collisionless MPD of SO2 will not occur at laser field strengths <20 GW cm ... 

Ab initio electronic structure calculation SCF" CF Quantum dynamics calculation" Experiment"... 

HCO is small enough to allow rigorous quantum dynamical calculations on the ground-state PES without any approximation or model assumption. 

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